We present a new fast vector penalty-projection method (VPPε ), issued from noticeable improvements of previous works [7, 3, 4], to efficiently compute the solution of unsteady Navier-Stokes/Brinkman problems governing incompressible multiphase viscous flows. The method is also efficient to solve anisotropic Darcy problems. The key idea of the method is to compute at each time step an accurate ...

We consider the Cauchy problem for 2-D incompressible isotropic elastodynamics. Standard energy methods yield local solutions on a time interval [0, T/ε] for initial data of the form εU0, where T depends only on some Sobolev norm of U0. We show that for such data there exists a unique solution on a time interval [0, exp T/ε], provided that ε is sufficiently small. This is achieved by careful co...

The mixed-order eigenvalue problem −δ∆u + ∆u + λu = 0 with δ > 0, modeling small amplitude vibrations of a thin plate, is analyzed in a bounded 2-D domain Ω that contains a single small hole of radius ε centered at some x0 ∈ Ω. Clamped conditions are imposed on the boundary of Ω and on the boundary of the small hole. In the limit ε → 0, and for δ = O(1), the limiting problem for u must satisfy ...

The purpose of this work is the development of a fully monolithic solution algorithm for quasi-static phase-field fracture propagation. Phase-field fracture consists of two coupled partial differential equations and it is well known that the underlying energy functional is non-convex and sophisticated algorithms are required. For the incremental, spatially-discretized problem, an adaptive error...

We consider a class of constrained optimization problems where the objective function is a sum of a smooth function and a nonconvex non-Lipschitz function. Many problems in sparse portfolio selection, edge preserving image restoration and signal processing can be modelled in this form. First we propose the concept of the Karush-Kuhn-Tucker (KKT) stationary condition for the non-Lipschitz proble...

We present a new fast vector penalty-projection method (VPPε) to efficiently compute the solution of unsteady NavierStokes problems governing incompressible multiphase viscous flows with variable density and/or viscosity. The key idea of the method is to compute at each time step an accurate and curl-free approximation of the pressure gradient increment in time. This method performs a two-step ...

This paper describes an exact ε-constraint method for bi-objective combinatorial optimization problems with integer objective values. This method tackles multi-objective optimization problems by solving a series of single objective subproblems, where all but one objective are transformed into constraints. We show in this paper that the Pareto front of bi-objective problems can be efficiently ge...

Abstract. Augmented Lagrangian method (ALM) has been popularly used for solving constrained optimization problems. Its convergence and local convergence speed have been extensively studied. However, its global convergence rate is still open for problems with nonlinear inequality constraints. In this paper, we work on general constrained convex programs. For these problems, we establish the glob...

Computational methods are considered for finding a point that satisfies the secondorder necessary conditions for a general (possibly nonconvex) quadratic program (QP). The first part of the paper defines a framework for the formulation and analysis of feasible-point active-set methods for QP. This framework defines a class of methods in which a primal-dual search pair is the solution of an equa...

An instance of a constraint satisfaction problem (CSP) is variable k-consistent if any subinstance with at most k variables has a solution. For a fixed constraint language L, ρk(L) is the largest ratio such that any variable k-consistent instance has a solution that satisfies at least a fraction of ρk(L) of the constraints. We provide an expression for the limit ρ(L) := limk→∞ ρk(L), and show t...